24 Projections Coordinate Systems

8/11/2019 24 Projections Coordinate Systems

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Ellipsoid: mathematical surface obtained byrevolving an ellipse about the earths polar axis

Selected to give a good fit to the geoid

Geoid: is the earths mean sea level surface

everywhere perpendicular to the direction of gravity,because of variations in the earths massdistribution, the geoid has an irregular shape.

Clarke Ellipsoid of 1866Geodetic Reference System of 1980 (GRS80)


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Lines of constant longitude are called meridians

Lines of constant latitude are called parallels


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Map Projections & Coordinate Systems

Map Projections: to convert geodetic positions of a portion of the earths

surface to plane rectangular coordinates, points are projected

mathematically from the ellipsoid to some imaginary developable

surface - plane that can be rolled out flat

Map Coordinate Systems:quantitative coordinate systems - based on

mathematical projection models, often a cartesian coordinatesystem (i.e. x, y axes) representing relative positions within a

particular map projection


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USGS 7.5 Topographic maps - coordinate systems

Geodetic (geographic): latitude, longitude (deg., min, sec.)State Plane: easting, northing (feet)

Universal Transverse Mercator: easting, northing (meters)

GLO, U.S. Public Land Survey: Township, Range, Section


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Lambert Conformal Conic Projection,

scales vary N-S,E-W oriented states: Penn, Tenn (31 states)

Transverse Mercator Projection,

scales vary E-W,N-S oriented states; Ill, Ind, Idaho (22 states)

MapProjections

Map projectionsuse different

models forconverting the

ellipsoid to a

rectangularcoordinate system.

Each generates

distortions in scale

and shape of

objects.

Cone vs. Cylinder


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Reference datums (horizontal, vertical) US Geodetic SurveyHorizontal and vertical datums consist of a network of control

monuments and bench marks whose horizontal positions and elevations

have been determined by precise geodetic control surveys.

NAD 27 - Clarke ellipsoid (1866), Meades Ranch origin (25k pt)

NAD 83 - GRS - 80 ellipsoid, Earths mass center (270k pts)

WGS 84

NGVD29 (26 sea level gauging stations US & Canada)

NAVD88 (625k km of control leveling, crustal movements..)

horizontal

vertical


Control point networks exist as

known points with ground

monuments (benchmarks)around the world


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Reference datums (horizontal, vertical) US Geodetic SurveyDatum transformations account for differences in geographic

coordinates due to changes in the shape or origin of the spheroid/

ellipsoid, and in some cases datum adjustments.

Map projections are usually considered exact transformations because

they are based on a specific mathematical formula (although someempirically based map projections also exist). Datum transformations are

considered empirical because they are based on data or survey points



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When transforming from

one map projection to

another that includes a

datum change, its usuallybest to first transform back

to Geographic coordinates

first, then re-project. See

Bolstad Fig. 3-47


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UTM


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Universal Transverse Mercator coordinate system: worldwide

coverage from 80 S lat to 84 N lat. Each zone is 6 wide in longitude,

60 zones worldwide

US UTM zones 10 (west coast) - 20 (east coast)

Map Projections & Coordinate SystemsUTM

U i l T M t


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Universal Transverse Mercator(UTM) Map Projection

In Idaho, we use the Boise CentralMeridian (117 Long.) for all easting

coordinates, and a false easting isadded so that all UTM easting

coordinates are positive within zone

11. Idaho UTM more recentlyestablished.


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State Plane


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Map Projections & Coordinate SystemsState Plane

M P j ti & C di t S t


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Rectangular: US PLSS


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The two major systems of legal land description used in the United States

are: (1) metes and bounds and (2) rectangular survey system.

The metes and bounds system was used in areas settled when the

U.S. was still a colony of England.

This system located tracts of land by describing the tract location toroads, trees, rocks, meanders or waterways, etc.





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Map Projections & Coordinate SystemsRectangular: US PLSS



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Irregularly shaped tracts and loss of markers as timepasses may cause many boundary disputes under this

system.

In 1784, the US adopted the rectangular survey system,which is used in 30 of the 50 states. This system is based on

meridians (north-south lines) and baselines (east-west

lines). There are 34 "principal meridians" in the United

States; each has a baseline associated with it.




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Tracts of land, called townships, are laid out beginning from

the point where the meridian crosses its baseline (initial point).Townships are as close to 6 miles square as possible.

6 mi.

T2S, R3W

Map Projections & Coordinate Systemsg



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The sections are numbered from 1 to 36, beginning in thenortheast corner. Each 1-mile square section contains

nominally 640 acres.

Section 14, T2S,R3W




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Areas smaller than a section are broken down into

quarters of sections or sometimes halves of sections.These tracts may then be further broken into quarters or

halves.

SE 1/4, NW 1/4,Section 14, T2S,

R3W



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What you should know:

ellipsoids fit to the earth geoid are used to create amodel of the earth

map projections are used to mathematically project the

ellipsoid onto a planar surface or flat map

we use reference datums and ground control networks

with monuments to connect real world locations tothese map projections and ellipsoids

what projections and coordinate systems (4) exist onour 7.5 minute topographic maps

use any of these map coordinate systems to determine

a position on our Moscow Mt. topographic map


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24 Projections Coordinate Systems

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